# Definitions - PowerPoint PPT Presentation

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Definitions. Given sets. Given sets : examples. To introduce declaration of a set of student ; [ student ] In a library management system, the type Book and Person can be introduced as given sets : [ Book, Person ]. Declaration of variables.

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Definitions

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## Definitions

### Given sets : examples

• To introduce declaration of a set of student ; [ student ]

• In a library management system, the type Book and Person can be introduced as given sets : [ Book, Person ]

### Declaration of variables

• A name is assigned a type when it is declared. Once a given set is declared, we can declare variables.

• Example

stud1 : Student --- declaring a student

library1 : pBook --- declaring a set of books

primes : p  --- declaring primes to be a set of integers

newestbook : Book   --- what the book is and a number

showing the copy

library : p(Book   ) --- declaring a library as a set of copies of

books

### Abbreviations

• Syntactic equivalence

• Example

basic_ref == {math, intro_to_computers}

• Is equivalent to the declaration basic_ref : p Book together with

the predicate basic_ref = {math, intro_to_computers}

### Enumerated types

• Use data type definition to introduce a type with a small number of members

• Name ::= list of elements separated by |

• Example

YesNo ::= yes | no

### Axiomatic description

• To introduce variables along with predicates giving further information